How to animate rotation of duplivert shape
You could use Dupliverts as an arranging tool, as you have already, working all at the origin, with the original plane's normal facing down its own local Y axis, (you may have to rotate it in Edit mode) as shown:



Then, to set up a basic rig:


With the circle selected, CtrlShiftA .. 'Make Duplicates Real'. Check 'Parent' The planes are now all instances, and can be transformed independently, but are all children of the circle.
Delete the original plane, and replace it with an empty at the origin.
Select a memorable plane-instance, and assign a Locked Track constraint to it. 'Target': the empty.'To':-Y. 'Lock': X
Select all the other planes, with the constrained one still active, and in the header  Object > Constraints menu, hit 'Copy constraints to selected' Now all the planes should be constrained to look at the empty.
CtrlP parent the empty to the circle
To tidy up, in the properties region of the 3D view, lock all the transforms of the empty, except Z location.
To tidy up further, select all the planes, and in an Outliner window, Alt-uncheck the selection arrow on one of them.




Now none of the planes should be directly selectable, the empty should only be able to move up and down in its local Z, (with the planes following), and the whole group can be moved or rotated by its parent circle.